三维非稳定温度场的p型自适应有限元分析

Analysis of p-version Adaptive Finite Element Method for Three Dimensional Unsteady Temperature Field

自适应是降低有限元计算结果对网格依赖性的有效途径,基于p型有限元法建立了三维非稳定温度场的自适应分析方法,自适应的策略采用单元升阶法,误差估计方法取温度的高阶计算值作为精确解的"最佳估计"。通过三维混凝土板算例,研究了绝热温升和放热系数、模型尺寸、计算时步长度、边界温差对计算误差和单元阶次的影响。结果表明:在边界温差不大时,绝热温升比表面放热系数对计算误差影响更大;在高阶计算中小尺寸模型比大尺寸模型误差明显减小;计算时步长的变化反映了温度场的时间梯度,越大的时步长需越高的计算阶数;模型边界的温差变化表现了温度场的空间梯度,越大的边界温差需越高的计算阶数。

Adaptation is an effective way to reduce the mesh dependence of finite element computation result. On the basis of the p-version finite element method, the adaptive analysis method for three dimensional unsteady temperature field is established. The adaptive policy is element order raising method. The error estimate selects the high-order temperature as the best estimate of precise value. According to a three dimensional concrete plate sample, the influence of some factors on calculation error and element order is researched, including the adiabatic temperature rise, heat transfer coefficient, model dimension, time step length and boundary temperature difference. The results show following conclusions. The adiabatic temperature influences calculation error more than heat transfer coefficient when the boundary temperattu＇e difference is low. The calculation error in small size model is less than in large size model when in higher order computation. The calculation time step length variation reflects the time gradient of temperature field, and the longer time step length demands higher order. The temperature difference variation of modal boundary shows the space gradient of temperature field, and the larger boundary temperature difference requires higher order.